If we sign an agreement where in exchange for my services you have to give me your first daughter, you can break the contract and refuse to pay, even if you signed it, because it's illegal.
In legal terms, a contract is an enforceable agreement; by definition if it is illegal or void or unenforceable, it is not a contract. Breach is a thing you do to a contract. Therefore you can't breach an illegal contract - you never had a contract.